Saxon Math 54 through Calculus

The Saxon Math series is hugely popular among homeschoolers, largely because it works so well for students working independently. The Math Intermediate series (for grades three through five) and the series reviewed here (Math 54 and up) are very different from the Saxon program for K-3.

Saxon two-digit grade level designations can help you figure out the correct grade level for each book, although free placement tests are available at their website. Typically the second of the two digits indicates the grade level usage for average to bright students. The first digit indicates the grade for students working a little below level. For example, Math 76 would be for average to bright sixth graders or for slower seventh graders.

Homeschool kits include a non-consumable student edition textbook, either an answer key or solutions manual, and tests with their answer keys. Some student books are hardcover and some softcover. For some high school courses, solutions manuals are available separately. There are no teacher editions for the Saxon program since each lesson in the student text provides the explanation of the concept to be learned. Each lesson includes an introduction and explanation of the new concept, examples and practice problems, then a set of problems that not only reinforces the new lesson content but also reviews previously-learned concepts. Parents might help students work through the beginning of the lesson, but most students will be able to work through lessons independently. Parents need to check daily assignments and tests, ensuring that students are understanding what they are learning. The program requires virtually no preparation time.

While most parents appreciate not having to directly teach this program, the newest editions have added a valuable feature that does require some interaction at the younger grade levels. The “warm up” box at the beginning of each lesson should be used orally. In that box typically are math fact drills, mental math problems, and a thought-provoking problem to solve....Warm-ups at high school level can be completed independently by students.

One significant feature of the Saxon series that sets it apart from many other math programs is the incremental method in which concepts are taught. Once a concept is introduced it is not dropped but is incorporated into the mixed practice that students encounter every day....Over time and through repeated exposure to a developing concept, students gain understanding and mastery....

In Math 54 and above, Saxon Math has a “rules” orientation in its presentation, more like A Beka’s rather than a hands-on conceptual orientation like Math-U-See and Moving With Math. Saxon’s own primary grades program by Nancy Larson is more conceptually oriented than these upper levels....

Even though the program is not strong on teaching concepts, thinking skills get a good workout. This means that the program works best for students who do not need manipulatives and who tend to figure out mathematical concepts without a great deal of explanation. It is also good for those who like “brain teasers” like those troublesome time/rate/distance problems.....

The situation with Math 87 and Algebra 1/2 is a little confusing. Math 87 was a late addition to the Saxon lineup, and was considered optional for a few years. However, with revisions to the other texts, Math 87 really replaces Algebra 1/2. Ideally, students will complete Math 87 in seventh grade and Algebra 1 in eighth. If a student is not ready for algebra in eighth grade, consider using Algebra 1/2 at that point. There will be some repetition of content but struggling students will be better prepared to tackle Algebra 1 if they complete both courses.

Math 65 Third Edition

This text is appropriate for the average fifth grader. Students who need extra time at this level might spend more time in this text, perhaps skipping the Algebra 1/2 book later on. It continues developing arithmetic skills through multiplication and division of fractions and decimals while reviewing and expanding concepts of place value, addition and subtraction, geometry, measurement, and probability. Powers and roots, prime and composite numbers, ratios, and order of operations are also taught....

Math 76 Fourth Edition

Math 76 is for average sixth graders or slower seventh graders. This text is especially good at providing a cumulative review and expansion upon topics covered through earlier grade levels. Among topics covered at this level are fractions, mixed numbers, decimals, percents, ratios, rounding, estimating, exponents, working with signed numbers, square roots, beginning algebraic expressions, surface area, volume, angles, circles, prime factorization, ratios and proportions, and statistics and probability....

Algebra ½ Third Edition

This pre-algebra text can be used after completing Math 87. Plenty of review, a spiral learning process, thought-provoking word problems, and clear instruction that works for independent study make this one of my favorite options available for this level, even if it is no longer needed....

Among topics covered are fraction, decimal, and mixed number operations; scientific notation, exponents, radicals, algebraic expressions and solving equations with one variable, working with signed numbers, order of operations, scientific notation, ratios, geometry fundamentals, and graphing. Saxon has resisted the inclusion of calculator instruction even though most other texts for this level include it....

Saxon Math High School Options

It is important to consider the design of the entire Saxon lineup of high school math courses before starting into Algebra 1. Fortunately, Saxon now has two options with two parallel series of textbooks.

Originally, Saxon took an approach that, while common to other countries, is uncommon in the United States. They integrated algebra, geometry, and trigonometry into three textbooks, titled Algebra 1, Algebra 2, and Advanced Mathematics. Most high schools teach one course in algebra, then geometry, then return to algebra. They have continued with this integrated approach with Algebra 1 and Algebra 2, Third Editions, now also referred to as the "Classic Editions." But they have recently published a brand new Geometry text and Fourth Editions of Algebra 1 and 2 that follow the more typical sequence. I will discuss the Third Editions first. Geometry required more space to review, so click here for that review.

Algebra 1 and Algebra 2 Third "Classic" Editions

....Algebra 1 coverage is comparable to that in other first year algebra texts.... The spiral method of presentation and constant review help students work fairly independently, a major advantage for parents who lack time and expertise....Overall, Algebra I is fairly easy for students to work through on their own....

If students have used Math 76 and Math 87, they might be ready for this book in eighth grade....

In the third editions, Saxon does an excellent job with algebra, but the geometry is weak in my opinion. Geometry is scattered throughout Algebra 1 and 2, and it is presented very briefly in both books. By the time students have completed both books they will have studied about one semester’s worth of geometry. They complete their geometry requirement with the Advanced Mathematics book. Explanation of geometry topics is fairly brief, and does not begin to compare with the quality of presentation in such texts as Discovering Geometry.

A student planning to take only one year each of algebra and geometry (not recommended for college bound students!) could use Saxon’s Algebra 1 Third Edition, possibly skipping over geometry instruction and problems, then switch to another publisher for geometry.

Students who complete both Algebra 1 and Algebra 2, but who do not intend to continue through Advanced Mathematics, need to use another resource to complete geometry requirements. So they, too, might skip geometry activities within Saxon’s first two books.

However, if a student is going to go through Advanced Mathematics, tackling a separate geometry course is likely to be redundant and overwhelming, so it would be better to stick with only the Saxon texts.

Algebra 2 Third Edition covers standard second-year algebra topics, although its inclusion of a significant amount of trigonometry is not a standard feature of all second year courses. Students will need a scientific calculator for this course....

Algebra 1 Fourth Edition

The Fourth Edition of Algebra 1 is a total rewrite rather than just a modification of the Third Edition. Both appearance and content are improved. The text has two-color printing throughout with more graphic design. Each lesson begins with a “warm up” that includes one vocabulary question and five review problems. “Investigations” follow every ten lessons. One of the most significant content changes is the early introduction and frequent use of a graphing calculator with graphing calculator labs. Also, probability and statistics receive far more attention in keeping with national math standards. In addition, the Fourth Edition introduces trigonometry and more extensive work with quadratic equations and functions than does the Third Edition.

One feature lost in the transition is the tongue-in-cheek content of some of the word problems. John Saxon often incorporated historically anachronistic references or just offbeat content such as “In a picaresque novel about the Spanish Main, the ratio of rascals to good guys was 13 to 5” (p. 149 2nd edition). The Fourth Edition has plenty of word problems and real life applications, but the humor has disappeared.

Other elements of Saxon’s methodology remain. Lessons are taught in increments followed by examples and a few practice problems. After that, students works on “Distributed and Integrated” Practice problem sets with 30 problems per lesson.

The homeschool package includes the student text, a Solutions Manual with complete solutions for the warm ups and all practice problems. A separate Homeschool Testing Book has 23 cumulative tests plus your choice of three, reproducible test answer sheets. In addition, a Test Analysis Form helps you identify the lesson for concepts tested in each problem in case review or re-teaching is needed. It also has the answers for all the tests. Note that the Classic Editions have answers to odd-numbered problems in the back of each student text, but there are no answers in the Fourth Editions. All answers and solutions are in the Solutions Manuals.

Algebra 2 Fourth Edition

The Fourth Edition of Algebra 2 is very similar in layout to Algebra 1 with the same course components. In keeping with the slightly advanced content of Algebra 1, Algebra 2 does much less review in the early chapters than in the Classic Edition. (A Skills Bank at the back of the book provides some review if needed.) Instead of a thorough review, this text jumps quickly into functions, matrices, and determinants. More attention is given to functions, while matrices and determinants are not even taught in the Classic Edition. Geometry is reviewed through problems and incorporated into lessons that apply algebra and trigonometry....A graphing calculator is used in every lesson with frequent Graphing Calculator labs ensuring that students become familiar with their use. This text should be a great option for those who need a challenging course that prepares them for more advanced math.

Saxon’s program has tended to be strong on skill development, but weaker on conceptual explanation and application. The inclusion of “investigations” in the Fourth Editions Algebra 1 and the new Geometry book (as well as in the newer texts for younger levels) reflects Saxon’s awareness of this problem. This particular feature along with other improvements would make the new Fourth Editions my recommended option.

Advanced Mathematics, Second Edition

Advanced Math should follow Algebra 2 for both the Third and Fourth Editions. This text is one of the easiest for most homeschoolers to work with to cover advanced algebra, geometry, and trigonometry. Originally designed to be a one-year course, Saxon now recommends that students take at least a year and a half to complete the course unless they are very bright. However, students who have worked through the fourth editions of Algebra and the new Geometry course should find more material to be at a "review" level and might be able to get through the text more quickly.

Advanced Math includes the equivalent of the second half of geometry, plus advanced algebra, pre-calculus, and trigonometry. In the revised second edition, much of the geometry was moved to the front of the book rather than being spread out. This should make it easier for students who need to get through the geometry in preparation for PSAT tests in their junior year. In addition geometric proofs are taught early on, then used throughout the first half of the book.

Students will need a graphing calculator to use with this text, although the calculator is not used as much as in other texts for this level....

Among other topics covered are logarithms, conic sections, functions, matrices, and statistics. This text moves even more into the theoretical math realm than do earlier Saxon texts.

By the time students complete Saxon’s Advanced Mathematics, they should be on a par with students who have completed a pre-calculus course....

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